PSAT Math : PSAT Mathematics
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Example Questions
Example Question #21 : How To Find The Solution To An Equation
If 3|x – 2| = 12 and |y + 4| = 8, then |x - y| can equal ALL of the following EXCEPT:
18
14
2
6
10
14
We must solve each absolute value equation separately for x and y. Remember that absolute values will always give two different values. In order to find these two values, we must set our equation to equal both a positive and negative value.
In order to solve for x in 3|x – 2| = 12,
we must first divide both sides of our equation by 3 to get |x – 2| = 4.
Now that we no longer have a coefficient in front of our absolute value, we must then form two separate equations, one equaling a positive value and the other equaling a negative value.
We will now get x – 2 = 4
and
x – 2 = –4.
When we solve for x, we get two values for x:
x = 6 and x = –2.
Do the same thing to solve for y in the equation |y + 4| = 8
and we get
y = 4 and y = –12.
This problem asks us to solve for all the possible solutions of |x - y|.
Because we have two values for x and two values for y, that means that we will have 4 possible, correct answers.
|6 – 4| = 2
|–2 – 4| = 6
|6 – (–12)| = 18
|–2 – (–12)| = 10
Example Question #1 : How To Find Out When An Equation Has No Solution
No solutions.
No solutions.
Cross multiplying leaves 
Example Question #31 : Algebra
If 
In evaluating, we can simply plug in 4 and 2 for 
Example Question #32 : Algebra
Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?
The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives
Example Question #31 : Algebra
John goes on a trip of 
If we take the units and look at division, 
Example Question #1808 : Sat Mathematics
With a 
In general, 
The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes 
Solving for 
Example Question #33 : Algebra
How much water should be added to 
Pure water is 0% and pure solution 100%. Let 
So the equation to solve becomes
and
Example Question #31 : Algebra
Solve 
This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of 
Solving this equation gives 
Example Question #71 : How To Find The Solution To An Equation
Joy bought some art supplies. She bought colored pencils for $1.25 per box and sketch pads for $2.25 each. Joy bought one more sketch pad than colored pencil boxes and spent $9.25. How many sketch pads did she buy?
Let 
So the equation to solve becomes 
Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.
Example Question #31 : Algebra
This question deals with absolute value equations which will normally gives you two solutions.
You need to solve two sets of equations for absolute value problems:
and
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